Waveguide support system

ABSTRACT

A system is disclosed for supporting a circular waveguide to minimize transmission losses caused by mode coupling resulting from the deflection of the waveguide due to its own weight between the supports. The conventional system of spacing the supports at regular linear intervals is replaced by this system which provides supports at varying linear intervals. The linear intervals vary to provide a uniform change in mechanical frequency (the inverse of linear spacing).

United States Patent [72] Inventor Robert P. Guenther Phlnlleld, NJ. [21] Appl. No. 885,418 [22] Filed Dec. 16,1969 [45] Patented Nov. 16, 1971 [73]- Assignee Bell Telephone LaboratorlesJncorponted Murray Hill, NJ.

[54] WAVEGUIDE SUPPORT SYSTEM 4 Claims, 3 Drawing Figs.

52 U.S.C1 333/95, 333/98, 333/98 M, 174/42, 138/106, 248/15 [51] lnt.C1 H0lp3/l2, HOlp 1/00, H023 7/14 so Field otSenrch 174/42; 138/106. 107; 248/15. 54. 345;:133/95. 955. 98 M [56] References Cited UNITED STATES PATENTS 2,225,334 12/1940 Daniels 174/42 2,694,101 11/1954 Shuhart 174/42 3,007,122 10/1961 Geyling 333/95 3,291,892 12/1966 Bethea, Jr 174/42 OTHER REFERENCES Timoshenko, S., Vibration Problems in Engineering 3rd Edition. 1955, '1A355T55 p. 342- 345.

Lanza; G.. Applied Mechanics, John Wiley & Sons, 1885, p. 555- 579.

Primary Examiner-Herman Karl Saalbach Assistant Examiner-Wm. H. Punter Attorneys-R. .1. Guenther and Edwin B. Cave ABSTRACT: A system is disclosed for supporting a circular waveguide to minimize transmission losses caused by mode coupling resulting from the deflection of the waveguide due to its own weight between the supports. The conventional system of spacing the supports at regular linear intervals is replaced by this system which provides supports at varying linear intervals. The linear intervals vary to provide a uniform change in mechanical frequency (the inverse of linear spacing).

PATENTEDIIIIII 16 mm SHEET 1 BF 2 F IG.

PRIOR ART PR/IcIIcAL Loss LIMIT MECHANICAL FREQUENCY (CYCLES/FOOT) FIG. 2

1 PRACTICAL oss LIMIT MECHANICAL FREQUENCY (CYCLES/FOOT) //\/l/ENTOR R. R GUENTHER A T TORNE V WAVEGUIDE SUPPORT SYSTEM BACKGROUND OF THE INVENTION This invention relates to circular waveguides and to means for minimizing transmission losses in long-distance guided wave systems.

It is well known that the propagation of electromagnetic wave energy in the fonn of the circular electric TE mode in circular waveguides is ideally suited to the transmission of high frequency, wideband signals over long distances since this transmission mode has a unique transmission characteristic, namely that the attenuation decreases with increasing frequency. Unfortunately, the TE mode is not the dominant mode supported in a circular waveguide. As a result, energy may be lost to higher and lower order modes which are also capable of being transmitted. In addition, it is desirable due to loss considerations to use a waveguide whose physical dimensions are substantially larger than those dictated by the cutoff frequency. Thus, a practical transmission system using a circular waveguide to transmit energy in the form of TE waves is inherently a multimode system.

Any geometric deviation in the waveguide itself is a source of transmission loss. The geometric deviations may be local ized, such as tilts, offsets or diameter changes occurring at the joints between sections of waveguide, or they may be continuous deviations, such as straightness deviation, diameter variation, ellipticity, etc. that vary smoothly along the distance of the guide. Any of these deviations causes a distortion of the wave field resulting in a coupling of the TE mode to the spurious modes of the multimode system. Although it is possible to filter the spurious modes, any energy transferred to those modes from the TE mode due to coupling will be lost in the filtering process. It is obviously preferable therefore to prevent coupling of the TE mode to the spurious modes as much as is practically possible.

An exhaustive study of the effects of random geometric imperfections on the transmission of the TE wave through circular waveguides was reported by Messrs. H. E. Rowe and W. D. Warters in an article entitled Transmission in Multimode Waveguide with Random Imperfections which appeared in the May I962 Bell System Technical Journal. It was their conclusion that the continuous straightness deviation appears to be the most serious tolerance in a waveguide system. Straightness deviation results primarily from three sources.

First, economic considerations require that some reasonable tolerance be permitted the manufacturer of waveguide pipe." As a result, some surface roughness, fluctuations in diameter, ellipticity, etc. will be present in the guide. The resultant losses must be tolerated if the tightest practical tolerances are already being maintained.

A second source of loss is occasioned by the practical tolerances that result from the placing of the waveguide and the effects of the joints in adjacent guide sections. Workmen cannot possibly lay waveguide so that each support is perfectly positioned and each joint perfectly aligned. These losses must also be tolerated since the increased cost of eliminating the losses thus introduced is prohibitive.

One other "inherent" loss must also be considered. In a paper entitled Circular Electric Wave Transmission through Serpentine Bends" which appeared in the Sept. 1957 Bell System Technical Journal, Mr. H. G. Unger discussed the losses introduced by the elastic deflection of a waveguide due to its own weight between supports of the system. Mr. Unger concluded that the conversion of TE, waves into the TM mode resulted in only a slight increase in TE attenuation. However, conversion to the TE mode could become seriously high at certain critical frequencies when the distance between supports is a multiple of the beat wavelength. Mr. Unger suggested two methods of controlling the resulting loss. The first suggestion is to permit the mode conversion and then filter the undesirable spurious modes using mode filters. This is effective; however, the energy converted to the filtered spurious modes is thereby lost. His second suggestion was to eliminate the periodicity of the support spacing. However, he suggested no practical method of doing so.

Ill]

SUMMARY or THE INVENTION The invention described herein relates to the nonperiodic spacing of the supports of a waveguide system and the selective placement of the supports so that the transmission losses are effectively controlled.

BRIEF DESCRIPTION OF THE DRAWING FIG. I shows graphically the relationship between the curvature power spectra and mechanical frequency for a uniform support spacing of l0 l0 feet;

FIG. 2 shows graphically the relationship between the cur vature power spectra and mechanical frequency for a support spacing that varies between l0 feet and 12.5 feet in accordance with my invention; and

FIG. 3 shows a physical representation of a waveguide support system embodying my invention.

DETAILED DESCRIPTION Since the radius of curvature of a supported waveguide is smallest at the supports, the mode conversion problem is also most critical at the supports. The effect of a continuous, but constantly changing, curve in the waveguide presents an inherently more complicated case to consider than does a discrete or constant curve. In the continuous case, the TE loss statistics may no longer be determined by the root mean square value of straightness deviation. It is essential now to consider the shape of the power spectrum due to curvature to predict the TE loss. Rowe and Warters in the above-cited paper determined that the loss caused by curvature in a waveguide with small difierential attenuation between the primary and spurious modes is given by the relationship where k the number of spurious modes (for a dielectric lined waveguide k=2, the TE and TM modes), cc,, the coupling coefficient between the primary and spurious mode, S,,(AB,,) the horizontal component of the power spectrum due to curvature, evaluated at the phase difference between the primary and spurious mode, and S,( A8,) the vertical component of the power spectrum due to curvature. It can be seen from the above relationship that the loss at any one frequency for any one spurious mode is directly proportional to the power spectrum due to curvature (curvature power spectrum).

The total curvature power spectrummay be defined as follows where the function k(x) represents the curvature and 0: represents the frequency in radians per unit length:

However, since 1),, the complex coefficient of a Fourier series, varies according to the relationship 1 L m Ia L mm: da: (3)

wit own] (5) where y, deflection at any point x in the 1* section E the modulus of elasticity I the moment of inertia of the beam W= weight density of the beam per unit length 5 d, the distance to the 1 support F, the force at the i" support M, the moment at the 1" support C, the slope at the 1'" support D, the deflection at the 1" support.

The following boundary conditions are known:

1 The slope and moment are continuous at each support.

2. The deflection is known at each support.

3. The slope is known at the two end supports. Therefore, the problem reduces to the simultaneous solution of 3N linear equations having 3N unknowns, where N is the number of waveguide spans. (N+l is the number of supports. After determining the value of M, and F,, the curvature k, may be detennined from the second derivative of the deflection equation, or

Hence, the relationship between the power spectrum and the waveguide curvature may be evaluated.

The optimum support system would be obtained by supporting the guide on a perfectly flat surface, or on very closely spaced supports, so that there was little or no intersupport deformation. However, the practical realities of permitting reasonable placing tolerance indicates that support spacing closer than approximately 10 feet is pointless. At closer spacing, the guide does not rest on each support since the deflection of the guide is less than the placing tolerance for the support.

Conversely, as the spacing is increased, the deformation of the guide between the supports increases with a resulting'rise in transmission loss. The indications are, therefore, that the minimum transmission loss would be obtained by providing supports at approximately 10-foot intervals, but not at regular, or periodic, spacing.

Statistically, random spacing would appear to be a solution to this problem. However, two additional problems are then encountered. Manufacture of a guide with spacing specified as random" would defy any realistic manufacturing process. Secondly, true random spacing means that some sections of guide will have very high loss, and other sections very low loss. The average would be an improvement over periodic spacing, but the loss in given sections would undoubtedly be well above workable limits.

Until now, no one has proposed a workable solution to this problem. However, I have invented a support system in which the spacing is increased from 10 feet to as high as 12.5 feet with a net decrease in loss, rather than the normally anticipated increase in loss. This is accomplished by selectively 55 varying the intersupport spacing according to the relationship:

where d distance to the next support d,, distance from the last support Af, an incremental change in mechanical frequency.

If, as is shown in FIG. 3, the supports are placed to provide a constant change in mechanical frequency (the inverse of the distance between the supports), rather than a uniform support spacing, the peaks on the power spectrum may be located where the transmission losses due to other factors are well below the tolerable limit, as is shown in FIGS. 1 and 2.

The graphical relationship shown in FIGS. 1 and 2 contrasts the differences between a system in which the supports are periodically spaced and a system. as shown in FIG. 3, in which 75 the supports are located according to my invention. It should be pointed out that in FIGS. 1 and 2, the curvature power spectra is plotted on a logarithmic scale wherein a difference of one unit" represents an order of magnitude. It should also be pointed out that only the losses due to the supports and defonnation of the guide due to its weight are shown. The actual loss would be somewhat higher because of unavoidable errors due to manufacturing and placement tolerances. How ever, the loss due to elastic defonnation represents the major portion of the total loss.

FIG. 1 shows the curvature power spectrum for a 2-inch diameter dielectric lined waveguide supported on uniformly spaced supports 10 feet apart (assumed zero-placing tolerance). The dashed reference line shows the practical al-- lowable transmission loss for a system operating at approximately 40-100 GHz. based upon the economic trade-off of attenuation loss versus repeater spacing. As may be seen, the loss due to the supports alone does not approach the practical limit until a frequency of approximately 0.20 cycles/foot.

However, referring now to FIG. 2, if the supports are located in accordance with my invention with the spacing varying continuously by 0.0005 cycles/foot so that the spacing between the supports changes from 10.0 feet to as high as [2.5 feet, the allowable loss limit is reached at approximately 0. l0 cycles/foot. The loss occurring below 0.10 cycles/foot may be ignored since the corresponding electrical frequency approximately Gl-lz. for 2-inch dielectric lined waveguide) is well outside the transmission band.

The relationship between support spacing and mechanical frequency is shown in the following table:

Naturally, the numerical values given are representative only. At different ranges of signal frequencies or different diameters of waveguide which are of course interrelated, the numerical values would not be the same. However, similar results would be obtained and the relationship would be consistent with that just described so long as a constant increment of change in mechanical frequency, Af,,,, is maintained for the system. If the value of Af,,, selected is too large, the number of steps from the maximum spacing to the minimum spacing becomes small, with the result that the spacing arrangement becomes effectively uniform once again. At the other extreme, if too small a value of Af,,, is selected, the changes in support spacing become quite small from one space to another. This necessitates more accurate tolerances in placement of the supports. At the same time, the number of steps between the maximum and minimum spacings becomes unworkably large. The resulting installation problems create the practical boundary condition for small values of Af What is claimed is:

l. A waveguide for the long-distance transmission of microwave signals comprising a conductive tube having a circular cross section, and

a plurality of supports for the tube, each support being selectively positioned along the length of the tube to provide a uniformly changing mechanical frequency wherein the intersupport spacing is nonperiodic so that the loss means at the other end of the waveguide for receiving the due to elastic deflection of the tube because of its wei ht transmission and for se aratin the communication 8 P 8 is controlled. signals from the carrier, and 2. A waveguide in accordance with claim 1 wherein a plurality of supports for the guide, the spacing of the supthe spacing between the supports varies according to the 5 ports being selected to provide a uniformly changing relationship mechanical frequency so that the transmission loss in- 1 troduced into the system by the elastic deflection of the n+r= guide due to its weight is controlled.

Af 4. A system in accordance with claim 2 wherein where 10 the spacing between the supports varies according to the d =the distance to the next support, relauonshlp d, the distance from the last support, and dmH 1 Af,, an incremental change in mechanical frequency. Af 3. A long-distance transmission system for communication d signals having a TE mode microwave carrier comprising 5 where a hollow-pipe waveguide having a circular cross section, i to the next suppon means at one end of the waveguide for generating the TE jg E' l frorln the last p f mode carrier and for inserting the communication signals w an mcremema change m mechamcal frequency" on the carrier,

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION 3 62lfl+85 Dated November 16, 1971 Patent No.

Inventor(s) Robert P. Guenther It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

Column 6, line 9, the claim reference numeral "2" should read -3.

Signed and sealed this 6th day June 1972.

(SEAL) Attest:

EDWARD M.FLETCI-IER,JR. Attesting Officer ROBERT GO'I'TSCHALK Commissioner of Patents OHM PO-QSU (In-F19) lbh- Ha 

1. A waveguide for the long-distance transmission of microwave signals comprising a conductive tube having a circular cross section, and a plurality of supports for the tube, each support being selectively positioned along the length of the tube to provide a uniformly changing mechanical frequency wherein the intersupport spacing is nonperiodic so that the loss due to elastic deflection of the tube because of its weight is controlled.
 2. A waveguide in accordance with claim 1 wherein the spacing between the supports varies according to the relationship where dn 1 the distance to the next support, dn the distance from the last support, and Delta fm an incremental change in mechanical frequency.
 3. A long-distance transmission system for communication signals having a TE01 mode microwave carrier comprising a hollow-pipe waveguide having a circular cross section, means at one end of the waveguide for generating the TE01 mode carrier and for inserting the communication signals on the carrier, means at the other end of the waveguide for receiving the transmission and for separating the communication signals from the carrier, and a plurality of supports for the guide, the spacing of the supports being selected to provide a uniformly changing mechanical frequency so that the transmission loss introduced into the system by the elastic deflection of the guide due to its weight is controlled.
 4. A system in accordance with claim 2 wherein the spacing between the supports varies according to the relationship where dn 1 the distance to the next support, dn the distance from the last support, and Delta fm an incremental change in mechanical frequency. 